Order-chain polytopes

Takayuki Hibi, Nan Li, Teresa Xueshan Li, Li Li Mu, Akiyoshi Tsuchiya

Abstract


Given two families X and Y of integral polytopes with nice combinatorial and algebraic properties, a natural way to generate a new class of polytopes is to take the intersection P = P1 ∩ P2, where P1 ∈ X, P2 ∈ Y. Two basic questions then arise: 1) when P is integral and 2) whether P inherits the “old type” from P1, P2 or has a “new type”, that is, whether P is unimodularly equivalent to a polytope in X ∪ Y or not. In this paper, we focus on the families of order polytopes and chain polytopes. Following the above framework, we create a new class of polytopes which are named order-chain polytopes. When studying their volumes, we discover a natural relation with Ehrenborg and Mahajan’s results on maximizing descent statistics.


Keywords


Poset, order-chain polytope, unimodular equivalence

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DOI: https://doi.org/10.26493/1855-3974.1164.2f7

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications